Andy H. Register

A MIMO radar benchmarking environment

With the growing amount of research being devoted to the concept of multiple-input multiple-output (MIMO) radar, there has been a lack of a common simulation and benchmarking environment for determining the viability and cost-effectiveness of MIMO radar architectures and algorithms. To this end, GTRI has developed a MIMO Benchmark environment to serve this purpose, which is to be made publically available to researchers in order to compare the performance of MIMO techniques with those of more conventional phased array radar systems. This paper describes the problem that the MIMO Benchmark is intended to be used to assist in solving, in the form of a new challenge problem for the MIMO community, as well as providing a summary of the architecture of the MIMO Benchmark infrastructure.123

Detection and diagnosis of radar modeling errors using covariance consistency

Often, detection-based tracking algorithms are developed without much regard for the effects of either the radars analog signal processing or its digital signal-processing algorithms. In this paper, we combine the effects of the radars signal processing and tracking algorithms to assess the combined effect on covariance consistency of various algorithms. To do this, we first define the terms detection, detection primitive, and measurement. Next, we provide a detailed dataflow diagram for the processing chain of an electronically-scanned radar so that we can examine the propagation of truth data through various coordinate frames relative to radar signal processing. We examine issues related to expressing truth data in different frames and different relationships among targets. We describe in detail many of the algorithms in the signal-processing chain of typical monopulse radar and finally analyze and demonstrate the covariance consistency of various algorithms in the radar processing chain. When properly applied, covariance consistency analysis can be used to detect and correct inconsistent algorithms, invalid assumptions, and coding errors. The techniques described in this paper provide insight in determining system covariance requirements and may be used to ensure that both the design and implementation of radar processing algorithms provide good covariance consistency. The example simulations provide a baseline for algorithm covariance consistency, examine some common approximations used to simplify radar simulations, and demonstrate the effect of implementation errors that actually occurred during model development.

A track purity approach for tracking metrics

Proper analysis of a simulated sensor tracking problem requires the ability to correctly determine the true trajectory that underlies each track. Traditionally, kinematic assignment of tracks to truth has been used. More recently, a “track-purity” approach has been proposed to both assess the performance of kinematic truth-to-track assignment algorithms and to overcome some of the anomalies that occur when kinematic assignment is used; particularly for unresolved closely-spaced targets. The track-purity approach relies on a simulations unique ability to identify which truth objects contribute to each measurement. Less clear are the following issues: 1) When a measurement is formed, what is the percentage contribution from each truth object in each measurement primitive, 2) How should truth contributions be combined and modified as measurement data are passed through the various data and signal processing algorithms found in a typical monopulse phased-array radar (e.g., closely-spaced unresolved objects, direction-of-arrival estimation, measurement clustering, data assignment, filtering, and multi-sensor fusion), 3) How should truth content values be used to produce a content-based association between tracks and truth? The complete process for establishing the truth content of a track from the initial truth content of each detection to the final truth content at the output of track filtering is discussed. This discussion includes the effects of measurement clustering and centroiding, ambiguity in the measurement-to-track assignment, filter gains used to update the tracks state estimate, and a truth-contribution-based method for establishing track-to-truth assignment. 1 2

Measurement-to-track cost assignment computation when tracking with the IMM estimator

In the multi-target tracking problem, the association of measurements to tracks is typically conducted using an m times n cost matrix, where there are m tracks and n measurements. Each element of this cost matrix is computed based on some measure of the statistical distance between the estimated track state and the measurement. A common approach is to calculate a negative log-likelihood value that includes the uncertainty of the estimate and measurement. When tracking with an interacting multiple model (IMM) estimator, multiple mode likelihood values are possible for each measurement/track pair. Computing the cost assignment matrix given these likelihoods is a critical design issue. This paper compares two approaches for computing the cost assignment matrix. The first computes the likelihood with the mode that maximizes the likelihood for each given measurement. An alternate approach evaluates the pure likelihood of the Gaussian mixture. To focus on data association, we assume that the objects are perfectly resolved. The impact of imperfect object resolution is reserved for future work

Continuous Time Simulation

Wind rustling the leaves, waves pounding the beach, the moon orbiting the earth, and a violin bow scraping across strings are a few examples of everyday events that carry on in a smooth, continuous way. Continuous M&S attempts to recon-struct this familiar real-world flow inside an environment that allows us change conditions, make measurements, and otherwise study various aspects of the sys-tem. Engineers use a wide array of models and techniques to predict the result of applying various inputs to a system. In general, there are three ways to build a continuous model and perform continuous simulations: scale models, equivalent component continuous models, and computer-based continuous models. Scale models and equivalent component models are analog techniques while computer-based models belong in the class of digital techniques. The use of different tech-niques is important because in complicated applications, analog models sometimes support the development of computer models and vice versa. Using different modeling techniques gives us a way to cross check answers and improves our ability to predict results. Successfully applying the right techniques to each new problem is part of the art and tremendous satisfaction that comes from working in the M&S field. This chapter will describe each of these three methods, but focuses mainly on the mathematics behind computer-based continuous models.

Introduction to Modeling and Simulation

Simulation is a multi-disciplinary approach to solving problems that includes mathematics, engineering, physical science, social science, computing, medical research, business, economics, and so on. Simulation is not new; it dates back to the beginnings of civilization where it was most commonly used in warfare. With the development of computers, simulation moved from role-playing, where people or toy soldiers represented the systems of interest, to computer-based simulation, where software is developed to encode algorithms that represent the systems of interest. Once referred to simply as simulation, the discipline is more often called modeling and simulation (M&S), emphasizing the importance of first modeling the system of interest before developing a computational representation. This chapter provides a brief introduction to M&S, and defines concepts such as model, simulation, and abstraction. It includes a discussion of the relationship between the real world, the model and the simulation, and includes a conceptual definition of simulation from an implementation perspective. The M&S pyramid, which is a construct for describing levels of resolution, will be introduced as well as the term Live Virtual and Constructive simulations, which is a way of describing how humans interact with simulations. Finally a brief primer on how M&S is used in systems engineering will be presented.

Monte Carlo Analysis

Many people think of a computer as just a fancy calculator; as a device that takes an input and calculates a value. Further, they think if you give a computer the same value over and over, it will always calculate the same result. Contrast this with everyday experiences of flipping a coin, throwing dice, and waiting in line. People savvy in modeling and simulation know that sophisticated software models often use random numbers to simulate probabilistic outcomes or other unpredictable effects. Models that rely on random numbers are called stochastic (as opposed to deterministic) and simulations that rely on random numbers are called Monte Carlo simulations. The first recognized use of Monte Carlo simulation in 1945 involved predicting the behavior of atoms in an atomic bomb. Since then, Monte Carlo techniques have been used for numerical integration and probability analysis, among others. This chapter will introduce Monte-Carlo methods, and demonstrate how the analysis is used for problems with many sources of uncertainty and a large number of dimensions.

Constructing Simple Hierarchies with Composition

There is another common form of inheritance, very different from parent-child inheritance, called composition. Using an object in composition is easy. All you have to do is assign an object as the value for a private member variable. For example, if double represents a class, we could say that this.mSize is one element of the composition. This means that even simple classes use a composition of built-in types. Complex classes add structures and objects to the composition. Unlike parent-child inheritance where the parents interface is public, the interface of every object in the composition remains private. In MATLAB, there is overlap between parent-child inheritance and composition. Parent-child inheritance is a special case of composition. The child is a primary object and the parent is a secondary object. This might seem backward but it is consistent with the way primary and secondary were defined. The parent is a secondary object because the parent object is stored as an element in the childs private structure.

Object Arrays with Inheritance

The paper states that with the introduction of cStar and cDiamond, the same class no longer represents both stars and diamonds. Even though both are derived from cShape and even though neither adds new features, cStar and cDiamond objects are different. These differences cast a big shadow on design because they force difficult choices between inheritance and vectorization.

Constructing Simple Hierarchies with Inheritance

The paper states that by using cShape function, it has drawn shapes that look like a star, a rectangle, and a diamond. Even though these three shapes have a lot in common, it is recognized as three different shapes. The inheritance builds a set of classes to recreate this taxonomy without copying a lot of code. Member functions common to all shapes are found only in cShape. Member functions with code tailored for each particular shape type are found in each particular directory. Inheritance is the glue that allows to build the hierarchy and allows MATLAB to find the appropriate function.